To find the volume of a triangular prism, you use the formula:

Volume=Area of triangular base×Length (height) of the prism\text{Volume}=\text{Area of triangular base}\times \text{Length (height) of the prism}Volume=Area of triangular base×Length (height) of the prism

Step-by-step process:

1. Calculate the area of the triangular base
   The area of a triangle is given by:

Area=12×base×height of the triangle\text{Area}=\frac{1}{2}\times \text{base}\times \text{height of the triangle}Area=21​×base×height of the triangle

where the base and height are the dimensions of the triangular face.

2. Identify the length (height) of the prism
   This is the distance between the two triangular faces (not the height of the triangle).

3. Multiply the base area by the length of the prism

Volume=(12×base×height of triangle)×length of prism\text{Volume}=\left(\frac{1}{2}\times \text{base}\times \text{height of triangle}\right)\times \text{length of prism}Volume=(21​×base×height of triangle)×length of prism

Example:

If the triangular base has a base of 10 inches and height of 7 inches, and the length of the prism is 3 inches, then:

• Area of the base = 12×10×7=35\frac{1}{2}\times 10\times 7=3521​×10×7=35 square inches
• Volume = 35×3=10535\times 3=10535×3=105 cubic inches

This gives the volume of the prism as 105 cubic inches

Additional notes:

• If you know the three sides of the triangle but not the height, you can use Heron's formula to find the area of the triangle before multiplying by the prism length.
• For triangles with two sides and an included angle, use the formula for area:

Area=12×a×b×sin⁡(θ)\text{Area}=\frac{1}{2}\times a\times b\times \sin(\theta)Area=21​×a×b×sin(θ)

then multiply by the prism length for volume

This method works for any triangular prism regardless of the triangle type.